I don't know how strict your budget is, or the age of your children, but here are my suggestions:
Breakfast
-Keep up with breakfast in the room. My DH and I find it much more relaxing, and it saves us time. Kids can be sold on in-room breakfasts as a time-saver and many of them enjoy the extra time in bed, anyway (big kids like it, too).
Beverages
-Cut down on the bought beverages. No adult beverages for you, no need to buy sodas or water. If you really dislike the tap water--I do--ask for a cup with water & ice at CS. It's free and you can fill your water bottles throughout the day. If you have to have the beverages, then share them. Most of us are drinking way too much soda anyway. (I'm guilty, guilty, guilty!)
Snacks
-If you can, cut out on the snacks. They're sooo expensive and unhealthy. [DH and I bought ice-cream sandwiches on our most recent trip to DLR out of nostalgia. 2 were $7.00...and huge...more than we needed.]
----Instead, bring in snacks: raisins, granola bars, peanut butter and crackers. I don't know your kids, but I think if you establish the snacks as special things you've chosen just for them--or have them help you pick snacks before you go to the park (or even in packing)--then you help establish their expectations. If you behave like snacks are a must, then that will translate to snacks being a must. (I know, I know, kids get that message without their parents' help too...)
---You might be able to find food containers with their favorite characters, Disney or otherwise, that become their special snack box. Then pack your homemade trail mix or whatnot in them.
---If you must have snacks, share them. I don't know how many are in your family, but you could easily split many snacks in half and have a tasty treat.
---And limit the number of snacks allotted. The first time I went to Disney I convinced myself I needed a midmorning, afternoon, and evening snack, plus a dessert with supper. What was I thinking? I convinced myself that I was walking so much that I needed the snacks.

This most recent, 5-day visit? We had three snacks, two of which we shared (after the ice-cream mistake). I know it's a hard sell, but maybe to get everybody on board you could print up snack coupons for Disney snacks (again, depending on your children's age). Once someone has used their snack coupon, that's it. It might encourage them to share snacks, too.
Portables
--Protein always works to stave off my hunger. Peanut butter sandwiches transport well, or peanut butter & crackers or peanut butter and celery, and Jif is now selling single-serving sizes. They're more expensive than jars of peanut butter but are very portable and cheaper than park food.
Dining In & Out of the World
-In terms of TS & CS meals, go offsite and look for more "bang-for-your buck." Other posters have talked about this. But commit to one or two dinners outside the park; it's a hassle, but can be a big savings.
---Character dining: You mentioned going to a "few" character meals. Wow. That seems to me to be a good place to cut your expenses. DH and I went to a character breakfast during this most recent trip--for the two of us it was over $50. I can't imagine what it is for a family. They fill you up, but I find I can't eat enough at one sitting to keep me sated for the rest of the day. If you normally do three, try to cut down to two or even one.
---I also agree that if you're going to do a character meal, make it a late breakfast/brunch/early lunch. Not only are they cheaper, but you might be able to eliminate the snacks more easily.
Overeating
-Finally, I agree with disneysteve. Portion sizes at many of the Disney places, and at restaurants in general, are big enough to share.